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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.InverseGaussianDist
public class InverseGaussianDist
Extends the class ContinuousDistribution
for
the inverse Gaussian distribution with location parameter
μ > 0 and scale parameter
λ > 0.
Its density is
The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.
Field Summary |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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InverseGaussianDist(double mu,
double lambda)
Constructs the inverse Gaussian distribution with parameters μ and λ. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double mu,
double lambda,
double x)
Computes the complementary distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double mu,
double lambda,
double x)
Computes the distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double mu,
double lambda,
double x)
Computes the density function for the inverse gaussian distribution with parameters μ and λ, evaluated at x. |
static InverseGaussianDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of an inverse gaussian distribution with parameters μ and λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getLambda()
Returns the parameter λ of this object. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [hat(μ), hat(λ)] of the inverse gaussian distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(double mu,
double lambda)
Returns the mean E[X] = μ of the inverse gaussian distribution with parameters μ and λ. |
double |
getMu()
Returns the parameter μ of this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double mu,
double lambda)
Computes and returns the standard deviation of the inverse gaussian distribution with parameters μ and λ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double mu,
double lambda)
Computes and returns the variance Var[X] = μ3/λ of the inverse gaussian distribution with parameters μ and λ. |
static double |
inverseF(double mu,
double lambda,
double u)
Computes the inverse of the inverse gaussian distribution with parameters μ and λ. |
void |
setParams(double mu,
double lambda)
Sets the parameters μ and λ of this object. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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inverseBisection, inverseBrent, inverseF |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public InverseGaussianDist(double mu, double lambda)
Method Detail |
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public double density(double x)
ContinuousDistribution
density
in class ContinuousDistribution
x
- value at which the density is evaluated
public double cdf(double x)
Distribution
x
- value at which the distribution function is evaluated
public double barF(double x)
Distribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary distribution function is evaluated
public double getMean()
Distribution
public double getVariance()
Distribution
public double getStandardDeviation()
Distribution
public static double density(double mu, double lambda, double x)
public static double cdf(double mu, double lambda, double x)
public static double barF(double mu, double lambda, double x)
public static double inverseF(double mu, double lambda, double u)
public static InverseGaussianDist getInstanceFromMLE(double[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(double[] x, int n)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parameters
public static double getMean(double mu, double lambda)
public static double getVariance(double mu, double lambda)
public static double getStandardDeviation(double mu, double lambda)
public double getLambda()
public double getMu()
public void setParams(double mu, double lambda)
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